This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A374149 #31 Aug 09 2025 04:02:03
%S A374149 5,5,4,5,0,8,4,9,7,1,8,7,4,7,3,7,1,2,0,5,1,1,4,6,7,0,8,5,9,1,4,0,9,5,
%T A374149 2,9,4,3,0,0,7,7,2,9,4,9,5,1,4,4,0,7,1,5,5,3,3,8,6,2,1,5,5,6,7,6,3,1,
%U A374149 5,1,1,5,7,0,4,7,2,5,6,1,2,4,2,6,8,0,1
%N A374149 Decimal expansion of the minimum volume of an axis-aligned bounding box which includes the shortest minimum-link polygonal chain joining all the vertices of the cube {0,1}^3.
%C A374149 It has been proved that it is not possible to join the 8 vertices of a cube with a polygonal chain that has fewer than 6 edges (see Links, Optimal cycles enclosing all the nodes of a k-dimensional hypercube, Theorem 2.2).
%C A374149 Here we are considering the additional constraint that asks to minimize the volume of the Axis-Aligned Bounding Box (AABB) including the above-mentioned optimal polygonal chain consisting of only 6 connected line segments and that joins all the vertices of the cube [0,1] X [0,1] X [0,1].
%C A374149 Given phi = (1+sqrt(5))/2, the well-known golden ratio (see A001622), a valid polygonal chain is (0, 1, 0)-(0, 0, 0)-((1+phi)/2, 0, (1+phi)/2)-(1/2, 1+phi, 1/2)-((1-phi)/2, 0, (1+phi)/2)-(1, 0, 0)-(1, 1, 0) (see Links, p. 164), and consequently the minimum volume AABB is [(1-phi)/2, (1+phi)/2] X [0, 1+phi] X [0, (1+phi)/2].
%C A374149 As noted by _Hugo Pfoertner_, the present sequence is also given by phi^5/2 (i.e., A244593/2).
%H A374149 Marco Ripà, <a href="https://doi.org/10.14710/jfma.v4i2.12053">General uncrossing covering paths inside the Axis-Aligned Bounding Box</a>, Journal of Fundamental Mathematics and Applications, Volume 4, 2021, Number 2, Pages 154-166.
%F A374149 Equals phi*(1+phi)*((1+phi)/2), where phi := (1+sqrt(5))/2 is the golden ratio.
%F A374149 Equals (11+5*sqrt(5))/4.
%F A374149 Equals phi^5/2.
%F A374149 Equals 10*A134944 + 3/2.
%e A374149 5.5450849718747371205114670859140952943...
%t A374149 RealDigits[(11+5*Sqrt[5])/4, 10, 100][[1]]
%Y A374149 Cf. A001622, A134944, A225227, A244593, A261547, A363755, A373537.
%K A374149 nonn,cons
%O A374149 1,1
%A A374149 _Marco Ripà_, Jun 29 2024